Republican House leaders on Wednesday were frantically trying to build support for a GOP proposal to avoid the year-end “fiscal cliff,” attempting to reassure a wary rank-and-file that taking the unprecedented step of allowing taxes to rise for those making more than $1 million a year is the party’s best option.

Leadership aides expressed cautious optimism that the plan, advanced by House Speaker John A. Boehner (R-Ohio) Tuesday, will pass the House in a scheduled Thursday vote.

But with the White House threatening a veto, arguing it does too little address deficits and does not ask enough of the wealthy, it is unclear how passage would resolve the fiscal crisis.

If Boehner is able to get the bill through the House, he would prove he has the sway with his own members to potentially deliver the votes for a deal with the White House, even one that raises tax rates.

But, it would be a disaster for him if he puts the plan to a vote Thursday and fails to win enough Republican votes for it to pass.

Boehner received significant cover Wednesday as Americans for Tax Reform, the anti-tax group headed by Grover Norquist, announced it will not consider a vote for the plan a violation of the pledge signed by 238 House Republicans promising never to raise taxes.

That’s because the bill would merely allow tax breaks enacted under President George W. Bush to lapse, not impose new taxes, and it spares those making less than $1 million a year from a tax increase.

“Republicans supporting this bill are this week affirming to their constituents in writing that this bill — the sole purpose of which is to prevent tax increases — is consistent with the pledge they made to them,” Americans for Tax Reform said in a statement.

But its passage remained uncertain. With Democrats dead set against plan, Republicans can probably lose only 17 votes, and a number of conservatives have spoken out against it.

“I still keep coming back to the fact that if we actually vote and say some taxes are going to go up on some Americans, I think that’s problematic,” said Rep. Jim Jordan (Ohio), chairman of the Republican Study Committee and a respected voice among conservatives. “We are the party that says you should not raise taxes.”

With two unrelated votes scheduled for Wednesday, top House Republicans will fan out across the House floor among members to gauge and cajole their support.

Boehner’s plan would allow the top tax rate to rise from 35 percent to 39.6 percent for those making more than $1 million a year.

It would not, however, replace automatic spending cuts set to take effect in January, a serious concern for hawkish Republicans concerned about a $50 billion cut that will hit the military without congressional action.

The plan also does not include additional spending cuts, as has been discussed in stalled negotiations between President Obama and Boehner over a broad deficit reduction plan.

“What kind of spending reductions are we getting in return? It’s pretty clear that there’s not a lot of that in this Plan B proposal,” Rep. Steve Womack (R-Ark.) said after being briefed on the idea Tuesday. He sounded potentially open to the idea but said the lack of spending cuts could divide the GOP.

Because of those concerns, Republican leaders were quietly polling members Wednesday to see whether they would find it easier to pass the measure if it were paired with a bill that outlined additional spending cuts. A meeting of the Rules Committee, which will set the terms of the Thursday floor debate, that was scheduled for 3 p.m. has been delayed to 5:30 p.m., as changes to the legislation are contemplated.

A handful of Republicans have already indicated publicly that they will reject Boehner’s proposal out of hand.

Rep. Raul R. Labrador (Idaho) called it a “terrible idea.” Rep. Tim Huelskamp (Kan.) said he, too, will vote no.

“I’ve said it again and again: You make certain that the Republicans end up in the minority here very quickly” if the GOP backs higher taxes, he said.

Rep. Justin Amash (Mich.), who like Huelskamp, has been tangling with Republican leaders in recent weeks after the two were removed from key committees for rebelling against party leaders, also opposes the bill.

The dilemma for conservatives is stark. If no bill passes, taxes will go up on nearly every American in January. But a bill that can pass both chambers of Congress is likely to include concessions many consider unacceptable.

And even if Boehner can muster enough Republican votes to pass his plan, it is unclear how the so-called Plan B would prevent the country from going over the fiscal cliff in less than two weeks. Senate Majority Leader Harry M. Reid (D-Nev.) has said it cannot pass the Senate.

That left many Republicans fretting about the logic of taking a tough vote that is unlikely to solve the crisis.

“This would be unprecedented,” said Rep. John Fleming (La.), noting that a Republican-controlled House has not voted to raise taxes since the passage of the 16th Amendment establishing the federal income tax. “So, the question becomes, if we’re going to go on record for raising taxes, what are we getting in return for that? Unfortunately, there are no spending cuts. We don’t expect this to be passed by the Senate, much less signed by the president. So, I have to question, why do we want to go on record as raising taxes on anybody when we’ve not done that in a hundred years?”

For many, their best option might be for Boehner to reach a deal with the White House that passes with votes from both parties — but over their objections.

“There are some who want to be able to vote no on any deal — but they want the deal to be the best possible deal,” said Rep. Patrick McHenry (N.C.).

McHenry said he believes conservatives must engage in the process to get a good deal. But he said it is difficult for Republicans to put their names behind a proposal many would have argued just weeks ago was a tax increase.

“This is a flat struggle,” he said.

For now, many are carefully listening to Boehner’s argument that agreeing to let rates rise on the ultra wealthy now would allow for a tactical retreat — letting Republicans push for the changes they want in entitlement programs and other spending cuts in coming months, when the president will seek to raise the debt ceiling and when a funding measure keeping government running lapses at the end of March.

“I’m very concerned about raising taxes without any spending cuts,” said Rep. Randy Hultgren (Ill.), one of 66 conservatives who voted against the deal to raise the debt limit in 2011. But, he added, “We know from the results of the election, revenues are going up. Taxes are going up at the end of the year if nothing happens. We’ve got to figure that out, how we minimize that in the best way possible.”